Method for measuring rheological properties and rheometer for carrying out the method

ABSTRACT

In a method of measuring rheological properties of a sample, an oscillation system containing the sample is caused to perform free oscillations, and the damping caused by the sample is determined, the rheological properties of the sample being possible to determine by means of the damping. By this method, rheological properties can be determined for samples of a small volume and/or low viscosity. The method is especially adapted to measure body fluids. A rheometer for carrying out the method is also disclosed.

The present invention relates to a method of measuring rheologicalproperties of a sample, and a rheometer for carrying out the method.

In medicine, rheology is a little used branch of science. The onlyexception is the measuring of the blood sedimentation reaction which formany years has been carried out to a large extent in order to checkwhether a person is sound. The blood sedimentation reaction is connectedto the viscosity of the blood.

However, it is known that the viscosity of other body fluids may also beaffected by a person's state of health. One knows, for example, thatchanges in the viscosity of the bile mirrors various states ofill-health in the liver and the biliary passages. Moreover, there is astrong connection between the function of the mucus in the bronchi andthe elasticity of the mucus. A further example is that cardiacinfarction is associated with an increase of the whole-blood viscosity.

It would thus be of interest if one could study in a simple manner theviscosity of different body fluids, such as blood, saliva, bronchialmucus, bile, semen, vaginal secretion, lachrymal fluid, synovial fluidand peritoneal fluid. However, today no apparatus is available for quickand simple registration of the viscosity of body fluids.

When measuring the blood sedimentation reaction, the sedimentation rateof the red blood corpuscles is determined by filling a test tube withblood and then allowing it to stand for about 1 h, whereupon the heightof the plasma column above the blood corpuscles is measured. Thismeasuring process is slow and cannot be used for other body fluids.

In industries, it is known to determine the viscosity of liquids bymeans of rotary rheometers.

A prior art, Couette-type rotary rheometer comprises two cylinders ofslightly different diameters, one arranged in the other. The outercylinder can be rotated by means of a drive, and the inner isstationary. The liquid sample whose viscosity should be determined isplaced in the gap between the cylinders. The viscosity of the liquidsample is determined by measuring the moment by which the liquid affectsthe inner cylinder as the outer cylinder is rotated and the liquid isshorn between the cylinders.

For a number of reasons, such a rheometer is however not suited for usewith body fluids since the volume of the fluid sample must be at least10 ml to produce accurate viscosity values. Some body fluids, e.g.synovial fluid, has a total volume in the body of this magnitude, andtherefore samples cannot be taken that are sufficient for thedetermination of viscosity.

Furthermore, some body fluids are of very low viscosity, in fact closeto that of water. The viscosity of such fluids cannot be measured bymeans of the prior art rheometer since the effect of the fluid sample onthe stationary cylinder is too small to be measured.

Finally, the prior art rheometer is far too expensive to make extensiveuse in medical attendance realistic.

One object of the invention therefore is to provide a method and arheometer for measuring rheological properties of a fluid, which makesit possible to determine the viscosity of low viscosity fluids and/orsmall volumes of fluid samples.

A further object of the invention is to provide a method and a devicewhich can replace the traditional measuring of the blood sedimentationreaction.

These objects are achieved by means of a method and a device having thecharacteristic features stated in the accompanying claims.

By causing an oscillation system containing the sample to perform freeoscillations and by measuring the damping of the oscillation, which iscaused by the sample, rheological properties of the sample can bedetermined. This principle can be generally used independently of thevolume and viscosity of the sample. The method according to theinvention can thus be used as an alternative to the known methoddescribed above.

The theory behind the invention is the following. Now assuming that ahollow cylinder whose inner radius is R and whose inner height is H issuspended by a torsion wire along its axis. The spring constant of thisconstruction is Iω₀ ², wherein I is the moment of inertia and ω₀ theangular velocity as the oscillation system with the empty cylinderperforms free torsional oscillations. The free torsional oscillationsare damped owing to the damping in the torsion wire and the othersuspension means. The damping is defined by the logarithmic decrement Δ:

    Δ=1/n (ln(A.sub.n /A.sub.1)),

wherein n is the number of periods of the oscillation, and A_(n) is theamplitude of the oscillation in the nth period and A₁ is the amplitudein the first period of oscillation.

If the cylinder is filled with fluid and the oscillation system iscaused to perform free torsional oscillations, the damping of theoscillation will be greater than in the case of an empty cylinder. Asthe cylinder oscillates, the oscillation will penetrate into the fluidin the cylinder. The penetration depth δ is determined by the viscosityη, the density of the fluid ρ, and the angular velocity ω according tothe formula

    δ=(η/ρω).sup.1/2

By selecting a suitable oscillation frequency, a penetration depth δ ofa low viscosity fluid can be obtained, which is much smaller than theradius R of the cylinder. In this case, the fluid in the centre of thecylinder will be immovable during the torsional oscillations and thefluid between the cylinder wall and the immovable portion of the fluidwill be shorn. The shearing action promotes the damping of theoscillation. The damping caused by the shearing action can be measured,and on the basis of the damping the viscosity of the fluid can bedetermined.

For a viscous fluid the following relationship applies, provided thatthe penetration depth δ is much smaller than the radius R and the heightH:

    η=2kωρ(Δ.sub.v -Δ.sub.0).sup.2   ( 1)

wherein Δ_(v) and Δ₀ are the logarithmic decrement in oscillation withand without fluid in the cylinder, and k is a calibration constant.

By measuring the damping and the relative frequency shift, the dynamicviscosity η' and the storage modulus G' can be determined for a slightlyelastic sample according to the following formulae: ##EQU1## is therelative frequency shift.

If the penetration depth is not much smaller than the radius R and theheight H, the formulae (1)-(3) are not valid. For determining therheological properties of a sample in this case, the cylinder isreplaced by e.g. a plate on which the sample is arranged, and a fixedabutment is caused to contact the sample, whereby the sample is shornbetween the plate and the abutment as the oscillation system performsfree oscillations. The presence of the sample in the oscillation systemgenerally results in a damping of the oscillation which, like before, isrepresented by a logarithmic decrement Δ, and a shift of the oscillationfrequency from ω₀ to ω. By measuring the damping and the frequency, thedynamic viscosity η' and the storage modulus G' can be determinedaccording to the following formulae:

    η=k.sub.1 (Δ.sub.V -Δ.sub.0)               (4)

and, in a first approximation,

    G'=k.sub.2 (ω.sup.2 -ω.sub.0.sup.2)            (5)

wherein k₁ and k₂ are calibration constants.

The present invention makes it possible to determine rheologicalproperties of samples having a small volume, since also small samplescause damping. To allow measuring of the damping in a reasonable time,the mass of the sample should preferably be an essential part of theoscillating mass in the rheometer.

The present invention further renders it possible to determinerheological properties of low viscosity samples. This is possible sincethe rheometer according to the invention has an insignificantself-damping as compared to the damping caused by the low viscositysample. As an example, it may be mentioned that the self-damping isabout 1% of the damping obtained when measuring a water sample.

The invention thus is well suited for use in determining the viscosityof blood and other body fluids.

Since a rheometer according to the invention is considerably lessexpensive to manufacture than prior art rheometers, the use of such arheometer for determining the viscosity of blood could replace thetraditional determining of the blood sedimentation reaction. In thiscase, the rheometer could be fitted with means for converting theviscosity values into blood sedimentation reaction values.

In the description of the theory behind the invention, the measuringcell, i.e. the cylinder, was suspended by a torsion wire, and theoscillation system performed free torsional oscillations. However, itwill appreciated that the free oscillations need not be torsionaloscillations, but that the corresponding damping is also obtained ine.g. pendulum oscillations.

The invention may be used to determine rheological properties ofmaterials having viscous and/or elastic properties. The materials can besolid, liquid, gaseous, plastic or gel-like.

In the following, the method and the device according to the inventionwill be described by means of an embodiment, reference being made to theaccompanying drawings in which

FIG. 1 is a part-sectional side view of an embodiment of a deviceaccording to the invention;

FIG. 2 is a top plan view of an embodiment of a device according to theinvention; and

FIG. 3 is a part-sectional side view of a second embodiment of a deviceaccording to the invention.

FIG. 1 illustrates an embodiment of a rheometer according to theinvention, which is adapted to measure samples having mainly viscousproperties, especially low viscosity fluids. The rheometer comprises astationary stand 1 having a bottom plate 2, three vertical legs 3 and anupper plate 4. A lower chuck 5 is attached to the bottom plate, and atorsion wire 6 is fixedly fastened to the lower end of the chuck.Torsion wires are commercially available and can be supplied withdifferent spring constants. The upper end of the torsion ware 6 isattached to an upper chuck 7 which is connected in axial direction to afree shaft 8 which via a coupling 9 is connected to a mounting 10 in theshape of a truncated cone. A measuring cell 11 is detachably arranged onthe mounting. As shown in more detail in FIG. 2, the measuring cell 11comprises a tubular hub portion 12 from which three supporting arms 13extend. At the ends facing away from the hub portion, the supportingarms 13 support a circular tube 14 which is adapted to contain a fluidsample. The tube 14 is circular in cross-section, and fluid can movefreely in the tube without being obstructed by partitions or likeobstacles while the boundary surfaces of the tube 14 are immovablerelative to each other, the boundary surfaces constitute the onlyboundary surfaces with which the sample is in contact during theoscillations. As an alternative to the measuring cell with the tubularsample space, a cylindrical or plate-shaped measuring cell could beused. The main thing is that the measuring cell is rotationallysymmetrical, and that the fluid can circulate in the sample spacewithout being obstructed.

The free shaft 8 is mounted in an air bearing 15 in the upper plate 4 ofthe stand. The air bearing 15 essentially consists of a porous carbonbearing, which is arranged with a gap round the free shaft 8. Compressedair is supplied to an outlet 16 and is injected through the carbonbearing and into the gap, the shaft being fixed with insignificantdamping of the oscillations. Air bearings are commercially available as"Porous Carbon Air Bearings".

A detector unit 17 for detecting the amplitude and frequency of the freeoscillation is arranged between the upper chuck 7 and the air bearing15. The detector unit is a so-called RVDT-unit (Rotational VariableDifferential Transformer) which is commercially available. It comprisesa primary winding 18, an armature 19 arranged on the free shaft 8, andtwo secondary windings 20 which are symmetrically arranged in angulardirection relative to the primary winding. The RVDT-unit 17 is connectedto a signal processing and calculating unit (computer 26).

The rheometer is further fitted with oscillation excitation means 21comprising an electromagnet 22 which is fixedly mounted on the stand 1,a first bar 23 which is movably mounted on the stand and biassed in aresting position by means of a spring 24, a second bar 25 mounted on thefirst bar 23, and a pin 26 arranged on the free shaft 8. When voltage isapplied to the electromagnet, the first bar 23 and the second bar 25arranged thereon are pulled towards the electromagnet 22, the second bar25 knocking into the pin 26 which causes the torsion wire 6, the freeshaft 8, the mounting 10 and the measuring cell 11 to oscillate. As soonas the voltage to the electro-magnet is disconnected, the bar 23 returnsto its resting position.

Alternatively, the RVDT-unit 17 may be used as excitation means, voltagebeing applied to one of the secondary windings for a short period oftime.

The essential thing about the excitation is that it is performed in thesame way on each occasion.

The function of the rheometer will now be described. Before being used,the rheometer is suitably calibrated for measuring a special fluid whoserheological properties are known or have been measured before by someother method. In the measuring operation, the measuring cell is filledwith a fluid sample, and the oscillation is excited by the excitationmeans 21. The damping of the oscillation is measured by means of theRVDT-unit 17, a sinusoidal AC voltage of about 5 kHz is applied to theprimary winding 19, and the differential signal from the secondarywindings 20, which arises owing to the unsymmetrical position of thearmature in relation to the secondary windings 20 during oscillation, ismeasured. The differential signal is demodulated by being sampledsynchronously with the AC voltage applied to the primary winding in sucha manner that a sample is taken in the same point in each period. Theroot mean square value of the demodulated signal is then converted intoa DC voltage signal which thus represents the oscillation amplitude.This DC voltage signal is A/D-converted and supplied to a personalcomputer which calculates the viscosity as follows. At a first and asecond predetermined level of the DC voltage, the number of samples isdetermined which has been taken until the DC voltage has decreased tothe current level. Since the sampling frequency is known, the time ittakes for the oscillation to be damped from the first to the secondpredetermined level can be determined by means of the number of samplestaken. Knowing the oscillation frequency, the logarithmic decrement forthe fluid sample can then be determined and, consequently, also theviscosity according to formula (1) on page 4.

The oscillation frequency can also be determined by means of theRVDT-unit 17 and, thus, also the relative frequency shift and thedynamic viscosity η' and the storage modulus G' according to formulae(2) and (3) on page 4.

In an embodiment of the rheometer which is intended for samples ofhigher viscosity or having more pronouncedly plastic or elasticproperties, the shown tubular measuring cell 11 is replaced by aplate-shaped measuring cell, and an abutment is arranged on therheometer so that the sample is shorn between the plate and theabutment. The abutment can be fixed on the rheometer. Thus, themeasuring cell comprises boundary surfaces 27 and 28 for the samplewhich are movable relative to each other, one surface being fixed bymeans 29 and the other movable such that the sample is shorn betweenthese surfaces during the oscillations, as shown in FIG. 3.

What is claimed is:
 1. A method of measuring rheological properties of asample, comprising the steps of:performing free oscillations of anoscillation system containing the sample, determining a damping of theoscillation, which is caused by the sample, measuring a frequency shiftof the oscillations, which is caused by the sample, and determiningrheological properties including viscosity and elasticity of the sampleby means of the damping and the frequency shift.
 2. The method asclaimed in claim 1, wherein the oscillations are torsional oscillations.3. The method as claimed in claim 2, further comprising the steps ofexciting the oscillations in such a manner that the oscillationspenetrate part-way into the sample, and that a portion of the sample isimmovable during the oscillations.
 4. A method of measuring rheologicalproperties of a sample, comprising the steps of:performing freeoscillations of an oscillation system containing the sample, includingexciting the oscillations in such a manner that the oscillationspenetrate part-way into the sample, and that a portion of the sample isimmovable during the oscillations, determining a damping of theoscillation, which is caused by the sample, and determining rheologicalproperties of the sample by means of the damping.
 5. A rheometer formeasuring rheological properties of a sample, comprising:an oscillationsystem includinga measuring cell for holding a sample, wherein themeasuring cell comprises boundary surfaces for the sample which aremovable relative to each other, one surface being fixed and the othermovable such that the sample is shorn between these surfaces during theoscillations, and an oscillation element to which the measuring cell isconnected and by means of which the oscillation system can be caused toperform free oscillations, and a detector for detecting the amplitude ofthe oscillations.
 6. The rheometer as claimed in claim 5, wherein avolume of the measuring cell is such that the mass of the fluid sampleis a substantial part of the oscillating mass in the oscillation system.7. The rheometer as claimed in claim 5, wherein the measuring cell isdetachably mounted.
 8. The rheometer as claimed in claim 5, wherein theoscillation element extends in a vertical direction.
 9. The rheometer asclaimed in claim 5, further including means for measuring the frequencyof the oscillation.
 10. The rheometer as claimed in claims 5, whereinthe measuring cell is closed.
 11. The rheometer as claimed in claim 5,wherein the rheometer is adapted to be used for measuring rheologicalproperties of body fluids.
 12. The rheometer as claimed in claim 11,wherein the rheometer is adapted to be used for measuring the viscosityof blood.
 13. A rheometer for measuring rheological properties of asample, comprising:an oscillation system includinga measuring cell forholding a sample, an oscillation element to which the measuring cell isconnected and by means of which the oscillation system can be caused toperform free oscillations, wherein the measuring cell is arranged on amounting element which is connected to the oscillation element, and anair bearing in which the mounting element is mounted, and a detector fordetecting the amplitude of the oscillations.
 14. The rheometer asclaimed in claim 13, further including means for measuring the frequencyof the oscillation.
 15. The rheometer as claimed in claim 13, whereinthe rheometer is adapted to be used for measuring rheological propertiesof body fluids.
 16. The rheometer as claimed in claim 15, wherein therheometer is adapted to be used for measuring the viscosity of blood.17. A rheometer for measuring rheological properties of a sample,comprising:an oscillation system includinga measuring cell for holding asample, wherein the measuring cell comprises boundary surfaces for thesample which are immovable relative to each other and which constitutethe only boundary surfaces with which the sample is in contact duringthe oscillations, the measuring cell having dimensions such that theoscillations penetrate part-way into the sample, and that a portion ofthe sample is immovable during the oscillations, and an oscillationelement to which the measuring cell is connected and by means of whichthe oscillation system can be caused to perform free oscillations, and adetector for detecting the amplitude of the oscillations.
 18. Therheometer as claimed in claim 17, further including means for measuringthe frequency of the oscillation.
 19. The rheometer as claimed in claim17, wherein the rheometer is adapted to be used for measuringrheological properties of body fluids.
 20. The rheometer as claimed inclaim 19, wherein the rheometer is adapted to be used for measuring theviscosity of blood.
 21. A rheometer for measuring the viscosity ofblood, comprising:an oscillation system includinga measuring cell forholding a sample, and an oscillation element to which the measuring cellis connected and by means of which the oscillation system can be causedto perform free oscillations, and a detector for detecting the amplitudeof the oscillations as a measure of viscosity values, and means forconverting viscosity values into blood sedimentation reaction values.